Radio controlled apparatus for air



April 1953 o. H. SCHUCK 2,635,167

RADIO CONTROLLED APPARATUS FOR AIR NAVIGATION Filed Feb. 28, 1949 7Sheets-Sheet l Y9 Znwentor l OSCAR HUGO SCHUCK Apnl 21, 1953 o. H.SCHUCK 2,636,167

RADIO CONTROLLED APPARATUS FOR AIR NAVIGATION Filed Feb. 28, 1949 7Sheets-Sheet 2 I E. Z

I 20 0.0. R. 2 s 2 a D.R. TRANSMITTER TRANSMITTER 2| BP L L I E L ME L'ATR'oTRN? EQUIPME OMNIDIREGTIONAL OMNIDIRECTIONAL RANGE RECEIVER RANGERECEIVER BEARING BEARING CONVERTER CONVERTER AZIMUTH AUTOMATIC COUPLINGPILOT UMT 33 Snventor AILERONSRJ OSCAR HUGO SOHUGK To ELEVATORS- TORUDDER M (Ittorneg April 21, 1953 0. H. scHucK 2,636,167

RADIO CONTROLLED APPARATUS FOR AIR NAVIGATION Filed Feb. 28, 1949 7Sheets-Sheet 4 I E. y 235 2B 1 f 231 ZIZ "2 220 f f r 2 I 227 292 2932l0. 226 236 I f 222 I A K 2" 234 L r 7 ms 1 o {a I I I I I I I 4501,275 m 27s l Q 2 55 I 296 201 40% 305 I L.. E E'1 BEARING 322 O2 303 357I 34l\3|8 344 354 am convan'ren 323 309 321 313 320 W 306 a 330 346 rINVERTERJ-3IT 9;

TO NAVIGATING COMPUTER Zinnentor OSCAR HUGO SCHUGK (Ittorneg April 21,1953 o. H. SCHUICK RADIO CONTROLLED APPARATUS FOR AIR NAVIGATION FiledFeb. 28, 1949 7 Sheets-Sheet 5 K mwnk m w w m s 1 E O I W 6 FL 1 u H.31.; R win M u u Q7 3 57 M 8w mu C A MMM 8e N9. w J/ m? 8n 3 an I ll mh7 mmm b0? Wan AT TORNE Y April 21, 1953 o. H. scHucK RADIO CONTROLLEDAPPARATUS FOR AIR NAVIGATION Filed Feb. 28, 1949 Nov won

INVENTOR.

OSCAR HUGO SCHUGK ATTORNEY Patented Apr. 21, 1953 RADIO CONTROLLEDAPPARATUS FOR AIR NAVIGATION Oscar Hugo Schuck, Minneapolis, Minn.,assignor to Minneapolis-Honeywell Regulator Company, Minneapolis, Minn.,a corporation of Delaware Application February 28, 1949, Serial No.78,865

6 Claims.

The invention relates to the field of navigational apparatus, and moreparticularly to improved radio responsive apparatus for use in aircraft.

In aircraft control it is already known to regulate the operation ofindividual craft so as to govern the attitude of the craft about threeaxes to bring about directed, level flight. Devices of this nature arereferred to as automatic pilots, and they function well as far ascontrol of a single craft is concerned.

The problem of coordinated control of numerous craft in a sizable areatranscends the capabilities of existing automatic pilots, however, andat present is handled by voice communication between the pilots of thevarious craft and supervisory operators at the control towers of thevarious airports. Instructions from the towers and the practice known asstacking supplement the scheduling and navigating procedures of thevarious individual flights to make their completion at a busy airport 2.practicable, if often protracted, process.

Automatic supervision of the craft in an area so that each, followingits schedule, arrives at the destination at such an instant that it canland immediately, without unduly cutting down the capacity of any runwayby precautionary delays, especially under overcast weather conditions,is a goal which is diflicult of achievement, but one which the presentinvention accomplishes.

Objects of the invention A general object of the invention is to provideimproved aircraft control apparatus by which a number of craft may betravelling toward an airport, by following radio signals, withoutincrease in the collision hazard as the airport is approached.

Another object of the invention is to provide improved aircraft controlapparatus, including radio actuated means, for enabling the pilots ofthe various craft to arrive at the airport at such intervals thatstacking at the airport of arrival is unnecessary.

A more specific object is to provide means, for installation in anaircraft, which is capable of deriving bearing data from the radiationsof a selected pair of radio ground stations, and of computing from thesedata the coordinates of the position of the craft at any time in acoordinate system which may be brought into a desired alignment with thepositions of the transmitting stations and with a desired ground path,

Another object of the invention is to provide means, as described above,capable of controlling the azimuth of the craft so that it follows agiven straight line path, and so that that path may be any selected oneof a number of mutually parallel paths.

Another object of the invention is to provide a navigating computercapable of deriving from the radio signals above described an outputproportional to the departure of the craft from a selected straight linecourse.

Another object of the invention is to provide a navigating computercapable of deriving from the radio signals above described an outputproportional to the distance from a craft to its destination.

Another object of the invention is to provide manually adjustable andautomatically radioresponsive computing means to give output voltagescorresponding to the components, along the X- and Y-axes of a Cartesiansystem, of the displacement of a craft carrying the computing means froman on-course position at the destination. Stated differently, thecomputing means determines from bearing radio signals, supplied by apair of Omnidirectional Ranges, and from manually adjusted settingscorrelating the computer with the terrain over which the flight is beingconducted, the off-track distance and the distance to destination of thecraft.

A specific object of the invention is to provide means for computing thevalues of m and y in the following equations:

where an, .120, w, ya and C are manually settable, while B1 and B2 areautomatically varied in accordance with bearing information received byradio.

Another specific object of the invention is to provide means forautomatically determining the quotient of two numbers, in which eachnumber is represented by an electric current flowing in a circuitincluding a resistor and one primary winding of a transformer, one ofthe resistors then being adjusted to vary the current in magnitude anddirection so as to reduce the magnetomotive force in the transformer tozero, and the amount of adjustment of the variable resistor requiredbeing taken as a measure of the quotient desired.

Yet another specific object of the invention is to provide means as justdescribed, in which the adjustment of the variable resistor is performedin accordance with the secondary voltage of the transformer.

A further specific object of the invention is to provide means as justdescribed, in which the dividend, or divisor, or each of them, comprisesa polynomial each term of which is represented by a voltage varied inaccordance with the magnitude of the term.

3 A further specific-object of the invention is to provide means wherebycertain of said terms may be varied as a tangent or cotangent functionof an angular variable.

Various other objects, advantages and features of novelty whichcharacterize my invention are pointed out with particularity in theclaims an reference should be had to the subjoined drawings, which forma further part hereof, and to the accompanying descriptive matter, inwhich is illustrated and described a preferred embodiment of theinvention. In the drawing:

Figure 1 is a diagram showing spatial relationships involved in thepracticeof the invention;

Figure 2 is a general. View of the elements making up an embodiment ofthe invention;

Figure 3 is a block diagram showing the functional relationship ofelements making up the system of Figure 2;

Figure 4 is asimilar showing of a converter for connecting theOmnidirectional Range receiver to the computer; and

Figures 5 and 6 show details of the azimuth and range components of anavigating computer according to the invention;

Figures 7 and 8 show mechanical details of a portion of the invention;and

Figure 9 is a sketch showing the functioning of the devices of Figures 7and 8.

The problem of azimuth control Figure 1 is in the nature of a map of anarea to be traversed by aircraft. From a stud of the terrain and aknowledge of trafiic requirements, it is first determined that thecenter line of a straight ground path between the. neighborhood of anairport of arrival and that of some distant airport of departure isalong the line I0. At suitable locations between the two air strips andwithin 50 miles of the line l0v radio ground stations Si and S2 areestablished. The area is charted, and there is superimposed upon thechart asystem of Cartesian coordinates the Y-axis of which coincideswith line Ill. The origin of the coordinates is spaced an arbitrarilyselected distance from the airport of destination to permit let-downmaneuvers. The geographic bearing C of the Y-axis is recorded, asarealso the coordinates $1, 111 and 0:2, 212 of the ground stations. TheX-coordinate of each station will be referred to as its offset, and theY-coordinate will be referred to as its onset.

A number of ground paths parallel to the center line It] and spacedtherefrom by intervals of say ten miles may now be laid out on thechart, in order to permit simultaneous movement of craft at differentspeeds and, if desired. in different directions. The X-coordinate orscheduled offset in each of these paths remains the same throughout itslength: one such path, having an absicissa an, is shown by line [3,which intersects the X-axis at D. The X-axis I4 is hereafter referred toas the terminus of arrival, since when this line is crossed a change inthe operation of the system must be made with the object of bringing thecraft to a landmg.

For simplicity of discussion thev showing of Figure 1 has been madespecial to the extent that the craft, the assigned track, and the twoground stations all he mathematically in the fourth quadrant: all theX-coordinates are thus positive and all the Y-coordinates are negative.As a practical matter any or all of these variables may lie in eitherthe third quadrant or the fourth quadrant, and the polarity of eachabscissa must be considered according to the quadrant in which it lies.The only ordinate which can ever be positive in a normal layout of thesystem is y presently to be defined, and this only if the craft goesbeyond the X-axis of the coordinates; that is if the craft overshootsits destination.

For purposes of illustration let it be assumed that the craft is orderedto follow the line I3. and that in fact it is at some moment located atpoint P, where its coordinates are mp, 31;). In such a case itsoff-track distance and has a value given by the following equation:

If an indicator of are is provided for the pilot of an aircraft he canmaintain the craft on a desired ground path simply by keeping the readinof the we indicator at zero.

One function of the invention is to determine the value of 17;) frominformation made available as a result of the radio transmissions fromstations S1 and S2. Each of these stations emits a radiation from whichthere can be determined the geographic bearing of the position of thecraft from the station: the bearings are indicated in Figure l by thesymbol B1 and B2 respectively. There are thus provided suflicient datato determine the value of (u according to the following mathematicalanalysis.

The point-slope form of the equation for a straight line in Cartesiancoordinates is Applying this formula to the straight lines passingthrough stations S1 and S2 in Figurev 1, the following equations result:

y=mia: (mum-g1) (3) and The craft is located at the point ofintersection x y of these lines. To evaluate 31;, in terms of $1, $2,111, 112, m1, and ma, let a:=:z: and y=y in the foregoing equations andsolve simultaneously for 20 and 111,):

Substituting these values in Equation 7 gives x $g Got: (B2 +931 coty2+y Means for computing ofi-track distance The general relation ofinstruments functioning to solve Equation 13 is shown in Figure 2. Theequipment at ground station S1 comprises the transmitter l5 of anOmnidirectional Range having a transmitting antenna system Hi. Theequipment at ground station S2 comprises the transmitter 2|! of anOmnidirectional Range having a transmitting antenna system indicated at2 The air-borne equipment includes a first Omnidirectional Rangereceiver 22 having a receiving antenna system 23, and a secondOmnidirectional Range receiver 21 having a receiving antenna system 3|].The term Omnidirectional Range refers to a specific radio unit known inthe art by that name and described in the J anuary 1942 issue of the RCAReview, volume 6, No. 3, pages 344 to 369.

The craft may be equipped with an automatic pilot 3|, and a navigatingcomputer 32 controls the automatic pilot, through a suitable azimuthcoupling unit 33, in accordance with the Omnidirectional Range signals,transmitted through bearing converters 34 and 35. Converters 34 and 35are necessary to make the electrical signals of the OmnidirectionalRange receivers available as mechanical motions to affect the computer,and azimuth coupling unit 33 is provided to modify the output of thecomputer according to its rate of change, and to derive therefrom inputssuitable to the nature of the particular automatic pilot of the craft.

As explained below, the output of bearing converter 34 is mechanicalrotation of a shaft 35 in proportion to the angle B1, and the output ofbearing converter 35 is mechanical rotation of a second shaft 31 inproportion to the angle B2. These shafts are represented in Figure 3 asinfiuencing the reading of an indicator 40 through a chain of authoritywhich includes further inputs from manual knobs 4|, 42, 43, 44, 45 and45 which are movable with respect to graduated scales. Knobs 4| and 42are adjusted in accordance with the magnitude of the X-coordinates x1and :02 of the locations of the ground stations. Knobs 43 and 44 areadjusted in accordance with the Y-coordinates yr and 112 of thelocations of the ground stations. Knob 45 is adjusted in accordance withthe X-coordinate at: of the desired ground path. Knob 46 is adjusted inaccordance with the value of angle C for the particular path beingflown.

The various functions performed in the navigating computer are suggestedby the various blocks in Figure 3, but it will be realized that numerousways of performing these functions, as electrical, mechanical,hydraulic, and so forth. will occur to those skilled in the art. Inconnection with Figures 4 and 5, later to be discussed, there will bepresented full disclosure of means for performing each of thesefunctions, and for the present only the relation of each to the overallresult will be considered.

As shown in Figure 3, the difference between the inputs from knob 46 andshaft 36 is taken in a subtractor 41 and applied to a cotangent device43 from which it emerges as an output 43 proportional to cot (Bl-C).This and an input from knob 4| are supplied to a multiplier 50, Theoutput 5| of the multiplier, having the value an cot (B1C) is suppliedto an adder 52 with inputs 53 and 54 from knobs 43 and 44.

The difference between the inputs from knob 45 and shaft 31 is taken ina second subtractor 55 and applied to a second cotangent device 56 fromwhich it emerges as an output 51 proportional to. cot (Ba-C). This andan output from knob 42 are supplied to a second multiplier 60. Theoutput 6| of the multiplier, having the value an cot (B2C') is alsosupplied to adder 52. Since the inputs 5 5|, 54, and 53 have the values:cz cot (B2C),:L'1 cot (B1C'),y2, and m, it is apparent that the output62 of adder 52 is the enumerator of the fraction on the right hand sideof Equation 12.

The outputs 49 and 51 from cotangent devices 48 and 56 are also suppliedto a subtractor 63, whose output 64 has a value the denominator of thesame fraction. Outputs 52 and 64 are combined in a divider E5, whoseoutput 55 is the right hand side of Equation 12 and is hence equal to seThis is combined with an input from knob 45 in a subtractor 6'1, whoseoutput 10 operates indicator 40 to a value (Mr-(H, or we, and may alsobe supplied as at H to azimuth coupling unit 33, the output of which isconnected to cause operation of automatic pilot 3|, whenever we is notzero, so as to cause the craft to return to the desired ground path.

The apparatus described above comprises means for maintaining a craft ona selected ground path and for indicating to a human pilot any departuretherefrom as it occurs, so that to a limited extent he is independent ofground landmarks, overcast weather, and variable cross winds. Theinformation is not sufficient, however, to give the pilot his locationin space, other than the knowledge that he is on a given line.

Spot supervision of distance travelled Then by substituting the slopevalues given in Equations 8-11 Equation 14 becomes by inspection. Anegative value for ya indicates that the craft is farther from itsdestination than it should be.

Inspection of Equation 15 above shows it to be of the same general formas that for w and the structure for performing the computation is verysimilar, as is shown in Figures 3, 4 and 5: it has many components incommon with the structure for determining :v

Means for determining distance to destination and ofi-schedule distanceSubtractor 41 in Figure 3 is shown as driving a tangent device 12 whoseoutput 13 is hence proportional to tan (B1-C'). This and an input fromknob 43 are supplied to a multiplier 14. The output 15 of themultiplier, having the value yi tan (B1C), is supplied to an adder 18,with inputs 11 and 80 from knobs M and 42.

The output from subtractor 55 is applied to a second tangent device 82from which it emerges as an output 83 proportional to tan (B2C). Thisand an output from knob 44 are supplied to a further multiplier 84. Theoutput 85 of the multiplier, having the value y2 tan (B2-C') is alsosupplied to adder 16. Since the inputs 8, 11, 15 and 85 have the value$2, an tan (Bi-C), and-ya tan (B2C'), it is apparent that the output83ofadder 16 is the numerator of the fraction on the right hand side ofEquation'15. The outputs 13 and 83 from tangent devices 12 and 82 arealso supplied to a subtracter 81, whose output 90 has a value tan (B1C)-tan (Ba-C) the denominator of the same fraction. Outputs 86 and90 arecombined in a divider 9|, which supplies outputs 92, and 93 equal to theright hand side 'of Equation 15 and hence to 3 Output 92 drives anindicator 96 displaying the value of 31 Output 33 is combined in asubtracter 91 with the output from a knob I00, and the output IOI of thesubtracter operates an indicator I02 to a value ypyi or yd.

The proper setting of knob I at any time may, for example, be determinedby the pilot from a previously prepared tabulation of Y-coordinateagainst elapsed time, or one of Y-coordinate against actual time for theparticular flight, and is correct only for an instant. At that instant,however, indicator I02 has a reading which is a measure of the distanceby which the craft is aheador behind its scheduled position. The pilotis thus given means for spot checking his progress along the ground pathfrom time to time against that required by his schedule, and he maydecrease or increase his air speed accordingly.

Indicator I02 in combination with the rest of the computer may'alsoserve a further useful function. If knob I00 is set to the Y-coordinateZlg of the terminus of departure, indicator I02 shows the number ofalong-track miles already travelled, while if knob I00 is set to theY-coordinate of the terminus of arrival, that is, to zero, indicator I02shows the number of alongtrack miles yet to be flown.

The Omnidirectional Range The Omnidirectional Range comprises in efiecta transmitter and a receiver for respectively emitting and responding toa high frequency carrier upon which are impressed a sinusoidal lowfrequency modulation and a keyed impulse voltage. At the transmitter anantenna array is so energized that the directions of maximum intensityof the carrier rotate about the antenna at the low frequency. Theimpulse voltage is transmitted when the positive. maximum of the carrieris due north of the transmitter, so that in any other direction from thetransmitter there is an interval between the instant of reception of thepulses and the instant when the carrier reaches its peak value.Thefunction of the Omnidirectional' Range receiver'is to'respond .tothi's interval by giving an indication of the direction of the receiverfrom the transmitter.

.261, and plates 210 and 21I.

Such portions of the structure of an Omnidirectional Range receiver asare necessary to an understanding of the present invention are shownabove the dotted line 200 in Figure 4. The principal components of thereceiver are a phase splitting bridge 203, a universal phase shifter204, a pair of pentodes 205 and 206, and an indicator 201 which isessentially a D. C. voltmeter with a center zero reading. Portions ofthe receiver, not shown, demodulate the carrier and feed the lowfrequency modulation to an automatic gain control circuit and afiltering amplifier. The output of the filtering amplifier, representingthe sinusoidal modulation of the carrier at the transmitter, appearsbetween conductors 2 I0 and 2I I in Figure 4. The received impulsevoltage appears between conductors 2I2 and 2I3, the latter beinggrounded.

Coupling capacitors 2I4 and 2I5 and conductors 2I3 and 2 I1 impress thefiltered low frequency modulation signal upon the input terminal 220 andHI respectively of phase splitting bridge 203, which comprises a pairoffixed capacitors 222 and 223 forming opposite arms of the bridge, anda pair of resistors 224 and 225 forming the remaining arms of thebridge. In order to permit adjusting the bridge so that the voltage atits output terminals 225 and 221 is out of phase with the voltage on itsinput terminals, resistors 224 and 225 are made adjustable by means 230.Voltages from terminals 22, 22I, 225 and 221 of the phase splittingbridge are made available to other portions of the system not heredescribed by conductors 23I and 232, 233 and 234, 235, and 236respectively.

The output of phase splitting bridge 203 is impressed upon universalphase shifter 204 in order to provide a voltage which may vary in phasethrough 360 degrees. Phase shifter 204 comprises an endless resistancewinding 231 tapped at four equally spaced points 240, 242, 24I and 243.Input terminal 220 of bridge 203 is connected to tap 240 of phaseshifter 204 by conductor 244 and resistor 245, terminal 22I to tap MI byconductor 243 and resistor 241, and terminals 226 and 221 to taps 242and 243 by conductors 250 and 25I.

Movable unitarily with respect to winding 231 are a pair of mutuallyinsulated sliders 252 and 253 carried by a suitable member 254 driven bya shaft 255 for rotation by operation of a manual knob 256: a scale 251is provided for indicating the rotated position of knob 256. Thearrangement is such that when slider 252 is in contact with tap 240 andslider 253 is in contact with tap 24I, the voltage between sliders 252and 253 is in phase with the voltage between conductors 2I0 and 2H. Whenthe sliders are rotated from this position by degrees the phase of thevoltage between them is 180 degrees from the input voltage, and as theyare rotated clockwise or counterclockwise from the zero position, thevoltage between the sliders correspondingly leads or lags the inputvoltage. Accordingly, as member 254 rotates clockwise from the positionwhere slider 252 contacts tap 240, the voltage between sliders 252 and253 varies in phase from a phase angle of 0 continuously through 260degrees of phase angle.

This continuously variable voltage is supplied to pentodes 25 and 203,comprising respectively cathodes 260 and 2'6I, control grids 252 and263, screen grids 264 and 235, suppressor grids 266 and Slider .252 is,con-

nected to suppressor grid 266 of pentode 205 by conductor 212, resistor213, and conductor 214: similarly, slider 253 is connected to suppressorgrid 261 of pentode 206 by conductor 215, resistor 216 and conductor211. Plate 210 of pentode 205 is connected to plate 211 of pentode 206by conductor 280, a resistor 281, a voltage divider 282, a resistor 283,and conductor 284, and positive plate potential is applied to the sliderof voltage divider 282, and to screen grids 264 and 265, from a suitablesource 285, the negative terminal of which is grounded at 286, as arecathodes 260 and 261. Bias voltage from a source 281 is supplied to thecontrol grids 262 and 263 through a pair of resistors 290 and 291, andto the suppressor grids 266 and 261 through phase shifter 204, bridge203, conductors 298 and 298', a pair of resistors 292 and 293 andconductor 299.

The impulse voltage is applied to control grids 262 and 263 of thepentodes through ground connections 213 and 266 and through conductor212, capacitor 294, and resistor 291, and is also made available toother portions of the system by a conductor 239. The impulse voltageprovides a fixed point in time with which comparison of the outputvoltage of the phase shifter 204 is to be made; the latter voltage isapplied to the pentode suppressor grids in opposite phase relation,while the impulse voltage is applied on the control grids of thepentodes in the same phase relation. When the phase shifter is set atzero the pulse coincides with the positive peak of voltage on onesuppressor grid, say that of pentode 205, and the negative peak ofvoltage on the other grid. If the phase shifter is rotated through 180degrees the pulse coincides with the positive peak of the voltage on thesuppressor grid of pentode 206, and the negative peak of the voltage onthe suppressor grid of pentode 205. With a unidirectional anode voltageand with suitable grid bias voltages, the arrangement causes thepentodes to discharge equally when the phase shifter is at 90 and 270degrees, moving from a maximum discharge of pentode 205 and a minimumdischarge of pentode 206 when the phase shifter is at zero through amaximum discharge of pentode 206 and a minimum discharge of pentode 205when the phase shifter is at 180 degrees.

Indicator 201 is connected between the plates of the pentodes byconductors 280, 295, 296, 291, 300 and 204. When the pentodes dischargeequally the indicator is at its central zero position: if pentode 205discharges more than pentode 206, the needle of the indicator swings tothe left while if pentode 206 discharges more than pentode 205, theneedle swings to the right. In other words, the voltage betweenconductors 295 and 300 is a unidirectional voltage of variable magnitudeand reversible polarity.

If the craft is due north of the transmitter, the pulse and the voltagepeak occur at the same time. For indicator 261 to give an on course orcenter zero indication, phase shifter 204 must be set to give a 90degree phase shift between input and output. This corresponds to theNorth indication of knob 256 on scale 251. If the craft is east of thetransmitter, the impulse precedes the voltage peak by an intervalcorresponding to 90 degrees of the low frequency. Adjustment of phaseshifter 204 to delay the voltage peak by 90 degrees causes the pentodesto again discharge equally. The instrument is designed to be used bysetting the phase shifter knob to the angle from which it is desired toapproach the station,

and then to fly the craft so that the indicator reading remains zero.

Construction of the bearing converter If means can be provided wherebyshaft 255 is driven always to such a position that indicator 201 readszero, the position of the shaft is then a measure of the bearing of thecrafts position from the transmitter. This adaptation of theOmnidirectional Range receiver is what converter 34 is designed toperform, and to this end the converter is mechanically connected toreceiver 22 and computer 32 by shafts 301 and 35.

Converter 34 comprises a pair of input terminals 302 and 303 connectedto the indicator by conductors 308 and 296, and 291 and 309, a pair ofpower terminals 304 and 305 of which the former is grounded as at 306,and a pair of output shafts 301 and 36 connected respectively to knob256 of the Omnidirectional Range receiver and to computer 85. Theprincipal components of the converter are an inverter 312, a motorcontrol amplifier 313, and a motor 314.

Inverter 312 comprises input terminals 316 and 311, output terminals 320and 321, and power terminals 322 and 323. Alternating voltage from asource 155 is applied to terminals 304 and 305 and hence by groundconnections 306 and 324 and conductor 318 to inverter 312, whichfunctions to convert unidirectional voltage applied to input terminals316 and 311 into alternating voltage appearing at output terminals 320and 321, the alternating voltage being of the frequency of source 155,and varying in amplitude and reversing in phase with variation in themagnitude and reversal of the polarity of the applied unidirectionalvoltage: such devices are known. Inverter 312 is connected to inputterminals 302 and 303 by conductors 325 and 326.

Motor 314 comprises a rotor 321 and a pair of stator windings 330 and331. Rotor 321 is mounted on a shaft 332 and unitary therewith is therotor 333 of a velocity generator 334 having a primary winding 335 and asecondary winding 336. Output shafts 301 and 36 are respectivelyconnected to shaft 332 through suitable reduction gearing 331 and 340.Quadrature capacitor 341 and phasing capacitor 342 are provided in thecircuits of windings 330 and 335, which are continuously energized fromsource 155. A capacitor 343 is connected across winding 331 of motor 314to improve its power factor: this winding is energized from the outputterminals 344 and 345 of amplifier 313 by conductors 346 and 241, theformer being grounded as at 350.

A voltage divider 351 comprising a slider 352 movable with respect to awinding 353 is connected across secondary winding 336 of velocitygenerator 334, and the output of this divider is applied, in series withthe output of inverter 312, to the input terminals 354 and 355 ofamplifier 313, through conductors 356 and 351 and ground connections360, and 361. Amplifier 313 is of the type in which a voltage output isobtained in the same phase and frequency as the voltage applied to itsinput.

Operation of the bearing converter Suppose the craft is at the locationP, with respect to the transmitter S1, shown in Figure 1; here thebearing of the craft from the transmitter is degrees measured clockwisefrom north. If phase shifter 204 is set at 85 degrees, pentodes 205 and206 discharge equally, conductors 295 11 and 300 are at the samepotential, and no voltage is applied to input terminals 302 and 303 ofinverter 35. The output from unit 3l2 is zero, and motor 3I4 isnotenergized for rotation.

If phase shifter 204 is setat some other value, the pentodes dischargeunequally, indicator 20'! gives a reading, and a unidirectionalvoltageis impressed on input terminals 302 and 303. This voltage isconverted to alternating voltage in inverter 3I2, and impressed uponamplifier 313, whose output energizes motor 3!4 to operate in onedirection or the other, according to the polarity of the input voltage.Operation of motor 314 rotates shaft 36 and readjusts knob 256 throughshaft 30! until it reads 85 degrees, the adjustment simultaneouslyaltering the phase of the pentode suppressor grid voltages to make-thepentodes discharge equally, at which point the voltage to the inverterdisappears, and the motor stops running. Velocity generator 334 servesto give the circuit antihunt properties.

By this means the position of shaft 36 is always a measure of thebearing of the craft from the transmitter: as the craft moves the phaserelation between the pulse and the phase shifter output changes, andoperation of motor 3l4 to correct the position of shaft 36 immediatelyresults.

The navigating computer Figures and 6 together show details of thestructure of navigating computer 32. The navigating computer isenergized at power terminals 365 and 36 6 with alternating voltage fromsource I55, the latter terminal being grounded at 31! and the formerconnected through a main switch 310 and a main fuse 368 to power bus389. The cross-track portion of navigating computer 32 comprises thesubject matterof Figure 5, and the along-track portion of the computercomprises the subject matter of Figure 6.

Structure of the cross-track portion of the navigating computer Powerbus 369 in Figure 5 is shown. to energize the primary winding 380 of atransformer 38! which for convenience of illustration is shown asdivided into two portions, one at the upper part of the figure includingsecondary windings 382, 383, 384 and 385 and another at the bottom ofthe figure including secondary windings 386 and 381. Mechanical inputsare supplied to this portion of the navigating computer along shafts 36and 37 from bearing converters 34 and 35, and along shaft 390 from knob46, which is manually operated in accordance with the required value ofthe angle 0. The rotations of shafts 36 and 390 are combined in adifferential 39!, having a first output shaft 392 and'a second outputshaft 393.

Shaft 392 actuates the slider 394 of a voltage divider 395, having apair of windings 396 and 39! center tapped at 398 and 399, andcomprising a part of cotangent device 48 of Figure 3. Its structure willbe given in more detail below.

Secondary windings 382 of transformer 30! energizes the winding 400 of avoltage divider 40!, having a center tap 402 and a slider 403, throughconductors 404 and 405. Slider 403 is connected to, one end of winding39 6 and one end of winding 3-91 by conductor 406, and center tap 402 isconnectedto the other ends of windings 39B and 39! by conductor 401.Slider 403 is adjustable along winding 400 by manual knob 4| to a valueproportional to -41: the voltage between'center tap 402 and slider 403is therefore also proportional to a:1, and of this voltage a portionproportional to the cotangent of B1C, determined by the position ofslider 394 on winding 395 or winding 39'! is taken and appears betweenslider 394 and a conductor 44'! connected to center taps 398 and 399.

The mechanical rotations of shafts 31 and 390 are combined in amechanical differential 4!!! having output shafts 4!! and -4!2. Shaft4!! is shown as driving the slider 4|3 of a second voltage divider 4!4having a pair of windings M5 and M5, center tapped at 4!8 and 4!8 andcomprising a part of cotangent device 56 of Figure 3.

Secondary winding 383 of transformer 38! energizes the winding 4! 6 of avoltage divider 4! 7, having a slider 420 and a center tap 42!, throughconductors 422 and 423. A conductor M9 is connected to center tap 42!and also to one end of winding 4! 5 and one end of winding MS of voltagedivider 4!4. Slider 420 is connected with the other ends of windings M5and 4 l 5 by a conductor 424, and'is adjusted by manual operation ofknob 42 in proportion to the magnitude of 032. Accordingly the voltagebetween center tap 42! and slider 420 is proportional to a. Of thisvoltage a portion determined by the setting of slider 413 on winding 4!5 or winding M5 is selected and appears between slider M3 and conductor408, which is connected to center taps 4!8 and 4!8. The voltage betweenslider M3 and slider 394 is accordingly the sum of an cot (B2C) and $1cot (B1-C) the difference in sign of the two values is brought about byconnecting the secondary windings 382 and 383 in the circuit in oppositephase as is suggested by the arrangement of the wires.

Secondary winding 384 energizes the winding 430 of a voltage divider43!, having a slider 432 and a center tap 433, through conductors 434and 435. Center tap 433 is connected with slider M3 by a conductor 436,and slider 432 is actuated by manual operation of knob 43 proportionalto the value of m. The voltage between slider 432 and center tap 433 isaccordingly proportional to 1/1, and by reason of the series connectionincluding conductor 436 this voltage is added to those previouslydescribed.

Secondary winding 385 energizes the winding 440 of a voltage divider 44!having a center tap 442 and a slider 443 through conductors 444 and 445.Center tap 442 is connected to slider 432 by a conductor 448, and slider443 is operated by manual adjustment of knob 44 in proportion to thevalue w: the negative sign for this quantity is obtained by reversingthe phase relationship of winding 385 with respect to winding 384, aspreviously discussed. Accordingly, a voltage appears between slider 443and center tap 442 which is proportional to y2, and by reason of theseries connection including conductor 446 is added to the voltagespreviously discussed.

A complete series circuit may now be traced from slide 394 through aportion of winding 395 or a portion of winding 39'! depending on theposition of slider 394, conductor 408, a portion of winding M5 or aportion of winding 4I5' depending on the position of slider M3, theslider, conductor 436, a portion of winding 430, slider 432, conductor446, a portion of winding 440 and slider 443. Slider 394 is connected bya conductor 44'! to the center tap 450 of a first primary winding 45! ofa transformer 452 having a further primary winding'453 and a secondarywinding 454. Primary winding 435 may have the same number of turns oneach half of primary winding 45L The ends of primary winding 45] areconnected by conductors 455 and 456 to the windings 451 and 466 of apair of variable resistors 46l and 462 having a common slider 463. Asshown, windings 451 and 460 are each circular in form and extendsubstantially 180 degrees around a circle. The windings are separated bytwo very narrow, oppositely disposed interruptions in the windings,which may be on a common form. Slider 463 is connected to slider 443 byconductor 464.

By the means described above, an alternating voltage which is the sum offour components is supplied to a circuit including the upper or lowerhalf of primary winding 450 and a variable portion of one or the otherof windings 451 and 460, depending on the position of slider 463. Theamplitude of this voltage is determined by the amount of resistanceadded in the circuit, and the phase of the voltage is determined bywhich half of the primary winding is being energized: both of thesefactors are controlled by the position of slider 463.

Output shaft 393 of differential 39! drives the slider 465 of a voltagedivider 466 having a pair of windings 461 and 469 center tapped at 469and 410, and comprising a part of cotangent device 46 of Figure 3.Windings 461 and 469 are energized from secondary winding 386 oftransformer 39! through conductors 41! and 412. Similarly output shaft412 of differential 4H1 actuates the slider 413 of a voltage divider 414having a pair of windings 415 and 418 center tapped at 416 and 419, andcomprising a part of cotangent device 56 of Figure 3. Windings 415 and418 are energized from secondary winding 381 of transformer 38! throughconductors 411 and 480. A conductor 48I joins slider 413 with slidercenter taps 469 and 416, and center taps 416 and 419 are connected withone end of primary winding 453 by a conductor 482, a resistor 483 havingthe same resistance as windings 451 and 466, and a conductor 484. Theother end of primary winding 453 is connected with slider 465 byconductor 465. By reason of the above connection it will be apparentthat a series circuit including resistor 493 and primary winding 453 isenergized from windings 366 and 381 in accordance with the sum of-cot(B1-C) and cot (Bz-C'), the amplitude of the voltage being determined bythe amplitude of the respective voltages. The voltage outputs fromsecondary windings 382, 383, 384, 385, 396, 381 are selected, asdiscussed below, so that the same constant of proportionality may beapplied to all the individual outputs, and the current in primarywinding 453 is proportional to the denominator of the right hand portionof Equation 12, the constant of proportionality being determined by themagnitude of the resistance 403. The current in the primary winding 45lof transformer 452 has been shown to be proportional to the numerator ofthe fraction in the right hand portion of Equation 12, and the constantof proportionality here is determined by the setting of slider 463.

The resistances of windings 451 and 460 are chosen to be high comparedto the resistance of windings 396, 391, 496, M5, 415', 416, 496 and 449.Similarly the resistance of resistor 463 is selected to be high comparedto the resistances of windings 461, 468, 415 and 416. A value of 100,000ohms is suitable for these resistances.

The current In flowing in primary winding 45! is related to the voltageVn between conductor 441 and slider 443, according to Ohms law, by

the expression Vn=InRn, where Rn is the total resistance in the circuitand in practice is the amount of winding 451 or winding 460 included inthe circuit. Similarly the current Id flowing in primary winding 453 isrelated to the voltage Va between center taps 416 and 419 and centertaps 469 and 410 by the expression Vd=Id-Rd, where Rd is essentially theresistance of resistor 483. If slider 463 is adjusted so that In isequal to Id, then Accordingly, Rn is a linear measure of the quotient.

Slider 453 is driven, through a suitable mechanical connection 486including reduction gearing 461, from a motor 490, including a rotor 49!carried on a shaft 492, and a pair of windings 493 and 494. Winding 493is energized from source I55 through power bus 369, quadrature capacitor495, and ground connections 496 and 31!. Winding 494 is energizedthrough conductors 491 and 500 from the output terminals 50I and 502 ofan amplifier 503 having power terminals 504 and 505 and input terminals506 and 501. Terminal 505 is grounded at 5|0, terminal 50! is groundedthrough conductor 491 and ground connection 496, and terminal 504 isconnected to power bus 369. Input terminals 506 and 501 are energizedfrom secondary winding 454 of transformer 452 by conductors 5H and 5l2.A phasing capacitor 498 is connected across winding 494.

Motor 490 operates under the control of amplifier 503 in a fashion wellknown to those skilled in the art. As long as no alternating voltageappears between input terminals 506 and 501 of amplifier 503, winding494 of motor 490 is not energized, and no rotation of shaft 492 takesplace. When an alternating voltage is impressed between input terminals506 and 501 of amplifier 503, winding 494 of motor 490 is energized, androtor 49! drives shaft 492 in one direction or the other, depending uponthe phase of the voltage across winding 494, which in turn depends uponthe phase of the voltage on input terminals 506 and 501. The connectionbetween shaft 492 and slider 463 is such that rotation of shaft 492 dueto voltage impressed on input terminals 506 and 501 of amplifier 503 isin a proper direction to change the current in primary winding 45!,compared with that in primary winding 453, so that the currents becomeequal. When this takes place, the fluxes in the core of transformer 452are equal and opposite, and no resulting voltage appears acrosssecondary winding 454. Operation of motor 496 accordingly isinterrupted.

Shaft 492 of motor 490 is also effective, through a further mechanicalconnection BIS which may include reduction gearing 5I4, to move theslider 515 of a voltage divider 5l6 whose winding 5|! is center tappedat 520. Windin 5l1 is energized through conductors 524 and 522 from onesecondary winding 523 of a transformer 524 having a further secondarywinding 525 and a primary winding 526. Winding 526 is energized fromsource I through ground connections 521 and 311 and power bus 369.Accordingly, the voltage between center tap 520 and slider M5 isdetermined by the position of the slider.

Secondary winding 525 of transformer 524 energizes, through conductors530 and 53!, the wind- 15 ing 532 of a voltage divider 533 having aslider 534 and a center tap 535. Center taps 520 and 535 are joined by aconductor 536. Sliders 515 and 534 are connected, by conductors 531' and546,

to indicator 46 which may conveniently take the form of a voltmeter.Slider 534 is actuated by knob 45.

The voltage between conductors 531 and 540 is also supplied at '11 toazimuth coupling unit 33 of Figure 2. The purpose of unit 33 is tosuperimpose control accordin to output 11 upon the particular automaticpilot being used, which may of course be electrical, hydraulic, or ofany other suitable type. Unit 33 may include means for adding to thesignal supplied by computer 32 a further component proportional to therate of change of the signal: for this purpose it may be desirable toconvert the alternating voltage to unidirectional voltage reconvertingit to alternating voltage after the rate component has been in serted,if desired. Arrangements suitable to this use are known.

One embodiment of structure capable of controlling the ailerons.elevators, and rudder of a craft in accordance with the signal at '11 isto be in my copending application, Serial No. 33,608 filed June 17,1948, and assigned to the assignee of the present application, where itis shown combined with an instrument landing system and a navigatingcomputer as well.

As pointed out above, Rn is a linear measure of the quotient beingsought. Sliders 463 and M are connected with haft 492 in such a mannerthat slider 515 is at center tap 526 when slider 463 is extending to theleft as seen in Figure 5, so that it does not engage either winding 45!or winding 4611. Windings 451 and 460 are both linear, so the amount ofrotation of motor 496 required to bring Rn to its desired value islinear, and the motion of slider 515 and the control of motor 496 isalso linear, and a measure of y Indicator 41] is therefore connectedacross two sources of voltage'in series, one being adjusted to a valueof (lit and the other to a value of x As suggested in Figure 5, thelatter voltage is connected in phase opposition to the former, so thatthe voltage applied to indicator 49 is proportional to a l-mt, that is,to we.

The circuit including potential divider 41H corresponds to multiplier 56in Figure 3. The circuit including voltage divider 41'! corresponds tomultiplier 60 in Figure 3. The circuit including primary winding 451 oftransformer 452 comprises adder 52 of Figure 3. The circuit includingthe primary winding 453 of transformer 452 comprises subtracter 63 ofFigure 3. Transformer 452, amplifier 563, motor 496 comprise divider 65of Figure 3, and voltage dividers 516' and 533 comprise subtracter 61 ofFigure 3.

Structure of the along-track portion of th navigating computer Thealong-track portion of computer 32, as shown in Figure 6, is generallyof the same nature as the cross-track portion just discussed inconnection with Figure 5. Alternating voltage is supplied from power bus369 through switch 518 and ground connections 519 and 3'11 to theprimary windin 560 of a transformer 581 having a plurality of secondarywindings 582, 583, 584, 585, 586 and 58]. This transformer liketransformer 381 in Figure 5, is shown divided. For clarity inillustrating the functional relationship, differentials 391 and 410, andinput shafts 36, 3'1 and396 are repeated in Figure 6; actually, only onesuch set -16 of mechanical inputs is provided in the computer, and thedifferentials are simply provided with additional output shafts 592,593, 611 and 612. Also only one set of knobs 41, 42, 43, 44 and 46 isprovided, as shown in Figure 2 although for clarity their knobs areshown in both Figures 5 and 6.

Shaft 592 actuates the slider 594 of a voltage divider 595 having a pairof windings 596 and 591 center tapped at 598 and 599, and comprising apart of tangent device '12 of Figure 3. Secondary winding 562 oftransformer 531 energizes the winding 669 of a voltage divider 691,having a center tap 692 and a slider 663, through conductors 664 and665. Slider 693 is connected to one end of winding 596 and the end ofwindin 591 by a conductor 696, and center tap 692 is connected to theother ends of windings 596 and 591 by conductor 697. Slider 693 isadjustable along winding 696 by manual knob 43 to a positionproportional to 1 1. A voltage accordingly appears, between slider 594and a conductor 64? connected to center taps 598 and 599, which isproportional in magnitude to 2/1 tan (Bl-C).

Mechanical output 6| 1 from difierential 4 I 0 actuates the slider 613of a voltage divider 614 having a pair of windings 615 and 615 centertapped at 618 and 618', and comprising a part of tangent device 92 ofFigure 3. Secondary winding 583 of transformer 581 energizes the winding616 of a voltage divider 611, having a slider 629 and a center tap 621,through conductors 622 and 623. Slider 626 is adjustable along winding616 by manual operation of knob 44, in proportion to the magnitude of'!/2, and is connected to one end of winding 615 and one end of winding6 I 5' by a conductor- 624. Center tap 621 is connected to the otherends of windings 615 and 615' by conductor 625. A conductor 6118connects center taps 618 and 618' with slider 594 of voltage divider595. Accordingly there appears between slider 613 and conductor 598 avoltage proportional to 11/2 tan (Bz-C). As previously pointed out thenegative sign is brought about by the phasing of the connections totransformer winding 583.

Secondary winding 584 of transformer 581 energizes the winding 636 of avoltage divider 631, having a slider 632 and a center tap 633, throughconductors 634 and 635. Center tap 633 is connected with slider 613 by aconductor 636. Slider 632 is actuated by manual operation of knob 42, sothat the voltage between slider 632 and center tap 633 is proportionalto $2.

Secondary winding 585 of transformer 5B1 energizes the winding 640 of avoltage divider 641 having a center tap 642 and a slider 643, throughconductors 644 and 645. Center tap 642 is connected to slider 632 by aconductor 646, and is actuated by a manual operation of knob 41 so thatthe voltage between slider 643 and center tap 642 is proportional to-x1.

Slider 594 is connected by conductor 64'! to the center tap 650 on afirst primary winding 651 of a transformer 652 having a further primarywinding 653 and a secondary winding 654. The terminals of winding 651are connected by conductors 655 and 656 to the windings 651 and 660 of apair of voltage dividers 661 and 662 having a common slider 663, thelatter being connected to slider 643 by conductor 664. The arrangementis such that there is applied, across a resistance determined inmagnitude by the position of slider 663 on winding 65'! or winding 666,a resultant voltage which is the sum of the 17 four voltages in tan(B1C') yz tan (Ba-C) x2, and r1. This sum is the numerator of Equation15.

Mechanical output 593 of differential 39I actuates the slider 565 of avoltage divider 655, having a pair of windings 53! and 668 center tappedat 559 and 6'13, and comprising a portion of tangent device T2 of Figure3. Windings 561 and 55B are energized from a secondary winding 585 oftransformer 58I through conductors Eli and 512. Accordingly thereappears between slider 665 and a conductor 685 connected to center taps659 and 513 a voltage proportional to tan (Bi-C).

Mechanical output BIZ from differential MU actuates the slider 613 of avoltage divider 615, having a pair of windings 575 and '13 center tappedat 616 and 619, and comprising a part of tangent device 82 of Figure 3.Windings 515 and 578 are energized from secondary winding 53? oftransformer 58I through conductors 61! and 385. Slider 673 is connectedto conductor 38L There appears between slider 613 and a conductor 582connected to center taps 675 and 5'13 a voltage proportional to tan(Bz-C).

Slider S55 is connected to one terminal of primary winding 553 byconductor 685, and center taps 676 and 319 are connected to the otherterminal of primary winding 653 by conductor 532, resistor 533, andconductor 68 3. Accordingly there is impressed across resistor 633 avoltage determined by the sum of tan (Bl-C) and tan (Ba-C).

The output of secondary winding 654 of transformer 552 is arranged tocontrol the operation of a motor 590, having a rotor 69I carried on ashaft 532 and a pair of windings 593 and 694. The winding 593 of motor690 is continuously energized from source I55 through power bus 353 andquadrature capacitor 695 and through ground connections 696 and 3H.Winding 694 of motor 590 is energized through conductors 69! and I03from the output terminals IBI and E02 and an amplifier I53 having powerterminals m and IE5 and input terminals I55 and 101. A phasing capacitor698 is connected across winding 695. Power terminals I04 and IE5 ofamplifier I03 are energized from source I55 through power bus 359 andground connections H3 and 3'. Input terminals I93 and I01 of amplifierI03 are energized from secondary winding 554 through conductors TI! andH2.

Motor 630 acts through a mechanical connection 686 including reductiongearing 381 to actuate slider 563 with respect to windings 551 and 663.Motor 690 also acts through a mechanical connection lI3 includingreduction gearing II4 to operate the slider H5 of a voltage divider IIBhaving a Winding III and a center tap I20. Winding H1 is energizedthrough conductors I2I and I22 from a first secondary winding I23 of atransformer I24, having a further secondary winding I25 and a primarywinding I25 energized from a source I55 through power bus 369 and groundconnections 12! and 3II Secondary winding I25 of transformer I24energizes, through conductors 135 and I3I, the winding I32 of a voltagedivider 133 having a slider I34 and a center tap I35. Center tap I35 isconnected to center tap I20 through a conductor 336. Slider I34 isarranged for actuation by manual knob I00. Sliders H5 and 134 areconnected by conductors I31 and I50 to indicator I02. Conductors I36 andI31 are also connected to indicator 36. 7

It will be obvious that thestructure of Figure 6 functions to solveEquation 15 in the same Way that the structure of Figure 5 functions tosolve Equation 13. Series electrical summing is utilized to giveseparately the numerators and denominators of the fractions, and thedivision is performed by the same ratio adjusting comparison method. Thedifferences between the two structures are simply those of phase,determining the polarity of quantities according to the equations to besolved, and substitution of tangent for cotangent devices where thesubstitution is needed.

The computer shown in Figures 5 and 6 is arranged to operate on a scaleof 10 miles per volt, and the secondary voltages required to be suppliedby transformers 38I and 58i are determined by this scale, and by themaximum values to be encountered in use. A practical range of values form1, m2, 111, yz, xt, yt is plus or minus miles: secondary windings 384,335, 584, and 585 must hence supply 20 volts.

The outputs from each of voltage dividers 395, M4, 595, and 5M must beten volts when knobs AI, 42, 53 and 64 are at 100 miles, and when angles(C'1C) and (32-0) are 45, since for these angles the tangent andcotangent are both unity. As a practical matter it is possible toconstruct devices Where each of these angles can be as large as are tan10.0: the output from each of windings 33L 382, 58I and 582 must hencebe 200 volts. If the number of turns in winding 453 is the same as thatin each half of winding 651, and if the resistance of resistor 483 isequal to those of windings 45! and 463, the outputs from windings 38Band 38! must be 200 volts. If the number of turns in winding 653 is thesame as that in each half of winding 65L and if the. resistance ofresistor 583 is equal to those of windings 651 and 350, the outputs fromwindings 586 and 587 must be 200 volts.

It is of course not necessary that the scale of voltage used in thestructure of Figure 5 be the same as that used in Figure 6, her need theoutputs of transformers 524 and I25 be on the same scale as those oftransformers 33I and 58L Nevertheless it is convenient to use one scalefor the entire computer, and the outputs of each of windings 523, 525,I23, and I25 under this arrangement is 20 volts.

The sliders in Figures 5 and 6 are shown in the positions they wouldassume when a craft being flown in accordance with the practice of theinvention actually was at the point P1. with respect to stations locatedas S1 and S2 as shown in Figure 1. From that figure it can be determinedthat x1=16 miles B1=86 322:8 miles B2=140 1 1=96 miles ast=64 milesy2=28 miles yr=-72 miles In the consideration of the data presented byFigure 1, a positive sign for an abscissa indicates that the point inquestion is to the right of the Y-axis, and a negative value of ordinateindicates that the point in question is on the rear side of the X-axis,both viewed from a craft moving along the course in the desireddirection. Angles are in all cases measured clockwise, and instantaneouspolarities areindic'ated by plus and minus signs at the ends of theseveral transformer windings.

The following voltage relations are found to exist in Figure VoltsOutput of winding 3S2 200 Voltage between slider 403 and center tap 40216 (402 positive) Voltage between slider 394 and center tap 398 43 (398positive) Output of winding 383 200 Voltage between slider 420 andcenter tap 421 8 (421 positive) Voltage between slider 413 and centertap 418 65 (4l8 positive) Output of winding 384 20 Voltage betweenslider 432 and center tap 433 9. 6 (433 positive) Output of winding 38520 Voltage between slider 443 and center tap 442 2. 8 (443 positive)Voltage between slider 463 and center tap 450 7.88 (450 positive) Outputof winding 386 200 Voltage between slider 465 and center tap 469 .27(469 positive) Output of winding 387 200 Voltage between slider 473 andc ter tap 476 80 (476 posit ve) Voltage between conductors 482 1.07 (480positive) Output of winding 523 20 Voltage between slider 515 and centertap 520 7. 35 (520 positive) Output of winding 525.... 20 Voltagebetween slider 53 and center tap 535 6. 40 (535 pos t ve) Voltagebetween conductors 537 and 540... 95 (540 positive) The followingvoltage relations are found to exist in Figure 6:

20 Indications of instantaneous polarity have been placed at the ends offorms 705 and 706 in Figure '7 to show the phase relation betweenvoltages applied across windings 396 and 397 by conductors 406 and 407.

Journalled in a bushing 714 moulded or otherwise fixed in base 700 is ashaft 7l5, axially positioned by a stop collar H6 and the hub N7 of acontact member 720, which are fixed to the shaft by set screws 727 and722 respectively. An arm 723 extends from hub H7, and a straight wire ofconducting material, comprising slider 394 of Figure 5, is supportedfrom arm 723 by suitable spring members 724 and 725. Conductor 447 isfastened to bushing 7|4 as shown in Figure '7, and electricalcommunication to slider 394 is thus established. The arrangement is suchthat the slider is resiliently urged into continuous engagement with oneor the other of windings 396 and 397 throughout a major portion of itsrotational movement. Shaft H5 comprises mechanical connection 392 ofFigure 5.

The arrangement is initially set up so that whenarm 723 is perpendicularto the direction of windings 396 and 397, it is aligned with center taps398 and 399. B1 and C are now set to such values that their diiference,Bl-C is 90, and hub H7 is fixed to shaft H5.

The foregoing description applies to voltage divider 395 of cotangentdevice 48. Voltage divider 466 is constructed in the same fashion,energized in the opposite phase, and installed according to the sameprocedure for driving by shaft 393. Voltage dividers 395 and 466 make upcotangent device 48 of Figure'3.

The structure used for voltage dividers 4M and 474, making up cotangentdevice 56, is the same. The slider of divider 414 is arranged fordriving from the indicated position in accordance with movement ofmechanical connection 4 from the position where B2C is 90, and the phaseof the energization of the divider is opposite to that of divider 395.The slider of divider 474 is arranged for driving from mechanicalconnection M2, and the divider is energized in the same phase as divider395.

In Figure 9 the resistance windings are shown as straight lines 730 and73!, everywhere parallel to and equidistant from a line X--X passingthrough the axis 0 of the contact. Several posi- Volts Output of winding582 200 Voltage between slider 603 and center tap 602 96 (602 positive)Voltage between slider 594 and center tap 598 35. 8 (598 positive)Output of winding 583.. 200 Voltage between slider 62 and center tap 28(620 positive) 3. 45 (318 positive) Output of winding 584 200 Voltagebetween slider 632 and center tap 4 633 0.80 (632 positive) Output ofwinding 585 20 Voltage between slider 643 and center tap 4 642 1. 60(642 positive) Voltage between slider 663 and center tap 650 40.0 (650positive) Output of winding 586 200 Voltage between slider 665 andcenter tap 669 87. 3 (665 positive) Output of winding 587 200 Voltagebetween slider 673 and center tap 678 12.3 (673 pos t ve) Voltagebetween conductors 682 and 685... 49. 6 (685 positive) Output oi winding723 20 Voltage between slider 715 and center tap 720 8.08 (715 positive)Output of winding 725 20 Voltage between slider 73 nd cen 735 7.2 (734pos t ve) Voltage between conductors 737 and 740... .88 (737 positive)The trigonometric devices numerals identifying them with device 48*,the

discussion is general, applying to all four of the units except asotherwise noted.

Each device comprises a pair of voltage dividers. Divider 395 comprisesa rectangular insulating base 700 having holes in its four corners formounting the device in any suitable fashion. fastened by recessed bolts703 and 704 .to the ends of the base, and to these blocks a pair oflinear insulating forms 705 and 706 are fastened by bolts 707, 708, 709and H0. Form 705 carries a uniform winding 396 of fine resistance wirecenter tapped at 398. Similarly, form 706 carries a uniform center.tapped winding 397.

' The structure and operation of the cotangent tions of the contact areshown, in which it engages the windings at point A, C, and E. Thevoltage between the center tap and the slider is measured by theprojection on the line X--X' 'of' the line joining 0 with the point ofcontact.

For the case of the point A this projection 0B has the value OB=AB cot4BoA,=0G cot x011 when the angle is measured counterclockwise Insulatingblocks l and 702 are from the direction OX. This remains true for anyangle Within 360.

algebraically proportional to the cotangent of the angle of displacementof the slider from a zero position along the line OX, except in twosmall ranges of extent 2:1. as shown. The magnitude of2a can be reducedby selection of a proper 21 ratio of the distance between the windingsto the length of the windings.

Figure 9 can also be used to illustrate the operation of the tangentdevices required in the practice of the invention: the only changesnecessary are reversal of the phase of the energization, indicated bythe parenthesized indicia of instantaneous polarity and the selection ofa new zero of direction, indicated by the line OY. Now

OD:DC cot 400D:

DC cot (90 LCOD =OG tanAYOC The structure thus can be adjusted to givean output algebraically proportional to the tangent of the angle ofdisplacement of the slider from the newly defined zero position, andvoltage dividers 595, EM, 666, and 616 may be initially adjusted andphased accordingly to make up tangent devices 12 and 82 of Figure 3.

Summary In the foregoing description and the annexed drawing I havedisclosed the details of structure of a computer for indicating, orcontrolling, or both indicating and controlling, the position of a craftwith respect to a set of coordinate axes. The apparatus automaticallycomputes the position of the craft when only its bearings from a pair ofpoints of known position on the set of axes, and the bearing of the axisof ordinates, are known. The structure includes a novel means ofperforming division automatically by separately computing the dividendand the divisor, representing them as electrical quantities, andequating these quantities by taking a variable portion of one forcomparison with the other, the magnitude of the portion required being ameasure of the desired quotient.

Numerous objects and advantages of my invention have been set forth inthe foregoing description, together with details of the structure andfunction of the invention, and the novel features thereof are pointedout in the appended claims. The disclosure is illustrative only,however, and I may make changes in detail, especially in matters ofshape, size, and arrangement of parts, within the principle of theinvention, to the full extent indicated by the broad general meaning ofthe terms in which the appended claims are expressed.

I claim as my invention:

1. In a device of the class described, in combination: first radioresponsive means giving an output determined by the direction of a craftfrom a first point of known position; second radio responsive meansgiving an output determined by the direction of said craft from a secondpoint of known position; means adjustable to give outputs varying inaccordance with the coordinates of said points on a set of coordinateaxes one of which is aligned with a path to be followed; meansadjustable to give an output varying with the direction of one of saidaxes; a first network comprising variable impedance means, a devicegiving an output in accordance with currents flowing therein, aplurality of sources of voltage variable in amplitude by said adjustablemeans and said radio responsive means, and means interconnecting saidmember, said device, and said sources so that current in said devicechanges with change in any of said means; a second rmpedance networkcomprising said output device, a further plurality of sources of voltagevariable in amplitude by said last named adjustable means 22... and saidradio responsive means, and means interconnecting said device and saidsources so that current in said device changes with change in any ofsaid means; and means varying said variable impedance means until thecurrents in said networks assume a desired relationship.

2. In a device of the class described, in combination: first radioresponsive means giving an output determined by the direction of a craftfrom a first point of known position; second radio responsive meansgiving an output determined by the direction of said craft from a secondpoint of known position; means adjustable to give outputs varying inaccordance with the coordinates of said points on a set of coordinateaxes one of which is aligned with a path to be followed; meansadjustable to give an output varying with the direction of one of saidaxes; a first network comprising variable impedance means, a devicegiving an output in accordance with current flowing therein, a pluralityof sources of voltage variable in amplitude by said adjustable means andsaid radio responsive means, and means interconnecting said device andsaid sources so that current in said device changes with change in anyof said means; a second impedance network comprising said output device,a plurality of sources of voltage variable in amplitude by said lastnamed adjustable means and said radio responsive means, and meansinterconnecting said device and said sources so that current in saiddevice changes with change in any of said means; and means varying saidvariable impedance means until the currents in said networks are equal.

3. In a device of the class described, in combination: first radioresponsive means giving an output determined by the direction of a craftfrom a first point of known position; second radio responsive meansgiving an output determined by the direction of said craft from a secondpoint of known position; means adjustable to give outputs varying inaccordance with the coordinates of said points on a set of coordinateaxes, one of which is aligned with a path to be followed; meansadjustable to give an output varying with the direction of one of saidaxes; a first network comprising a device giving an output in accordance with currents flowing therein, a plurality of sources of voltagevariable in amplitude by said adjustable means and said radio responsivemeans, and means interconnecting said device and said sources so that afirst current in said device changes with change in any of said means,and variable means for changing the amplitude of said current andreversing its sense in said device; a second impedance networkcomprising said output device, a plurality of sources of voltagevariable in amplitude by said last named adjustable means and said radioresponsive means, and means interconnecting said device and said sourcesso that a second current in said device changes with change in any ofsaid means; a motor; means connecting said motor to said variable meansfor operation thereof to make said first current equal and opposite tosaid sec ond current; and motor control means energizing said motor inaccordance with the output of said device.

4. Means for determining a coordinate of the location of a craft withrespect to a pair of axes, one of which is aligned with a path to befollowed, when its bearings from each of a pair of fixed stations, thebearing of one of said axes, and the coordinates of the locations ofsaid stations are known, comprising, in combination: means adjustable inaccordance with each of said'bearings; means giving first and seconddifierence angle outputs proportional to the differences between each ofsaid first named bearings and said second named bearing; means giving afirst output proportional to a discontinuous trigonometric function ofsaid first difference angle output, and a second output proportional tothe same function of said second difierence angle output; means giving afirst pair of outputs proportional to the coordinates of said firststation, and a second'pair of outputs proportional to the coordinates ofsaid second station; means giving a third output, proportional to theproduct of said first output and one of said first pair of outputs, anda fourth output, proportional to the product of said second output andone of said second pair of outputs; means combining said third andfourth outputs with the other outputs of said first and second pair togive a dividend output; means combining said first-and second outputs togive 7 a divisor output; and means combining said dividend and divisoroutputs to give a quotient output which is the desired coordinate of thelocation of said craft.

5. Means for determining a coordinate of a craft with respect to apair'of axes, one of which is aligned with apath to be followed, whenits bearing is known from each of a pair of fixed stations of knownlocation with respect to said axes, and when the bearing of one of saidaxes is also known, comprising, in combination: means adjustable inaccordance with the abscissa and ordinate of the location of eachstation, means adjustable in accordance with each of said bearings;means subtracting said last named bearing from each of said first namedbearings to give first and second difierence angles related to saidfirst and second stations respectively; means giving first and secondoutputs proportional to the cotangents of said first and seconddifference angles; means giving third and fourth outputs and fifth andsixth outputs proportional respectively to the abscissa and ordinate ofthe location of said first station and the abscissa and ordinate of thelocation of said second station; means giv-' ing seventh and eighthoutputs proportional to the product of said first and third outputs andthe product ofsaid second and fifth outputs, means combining saidfourth, sixth, seventh and eighth outputs to give a dividend output;means combining said first and second outputs to give a divisor outputand means combining said dividend output and said divisor output to givea final output which is the quotient desired.

6. Means for determining a coordinate of a craft with respect to a pairof axes, one of which is aligned with a path to be followed, when itsbearing is known from each of a pair of fixed stations of known locationwith respect to said axes, and when the bearing of one of said axes isalso known, comprising, in combination: means adjustable in accordancewith the abscissa and ordinate of the location of each station; meansadjustable in accordance with each of said bearings; means subtractingsaid last named bearing from each of said first named bearings to givefirst and second difference angles related to said first and secondstations respectively; means giving first and second outputsproportional to the tangents of said first and second difference angles;means giving third and fourth outputs and fifth and sixth outputsproportional respectively t-o'the abscissa and ordinate of the locationof said first station and the abscissa and ordinate of the location ofsaid second station; means giving seventh and eighth outputsproportional to the product of said first and fourth outputs and theproduct of said second and sixth outputs, means combining said third,fifth, seventh and eighth outputs to give a dividend output; meanscombining said first and second outputs to give a divisor output; andmeans combining said dividend output and said divisor output to give afinal output which is the quotient desired.

' OSCAR HUGO SCHUCK.

References Cited in the file of this patent UNITED STATES PATENTS NumberName Date 2,137,847 Libman Nov. 22, 1938 2,468,179 Darlington et al.Apr. 26, .1949 2,472,129 Streeter June 7, 1949 2,488,448 ,Townes et a1Nov. 15, 1949 2,541,277 Omberg et al Feb. 13, 1951

